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Semicircles are constructed on AB, AC, and BC.  A circle is tangent to all three semicircles.  Find the radius of the circle.

 

 Mar 31, 2024
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The radius of the circle is r.

(r+1)2=(2r)2+12r2+2r+1=44r+r2+16r=4r=23

laugh !

 Mar 31, 2024

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